Method and appartus for generating curves



Oct 15, 1946. R. w. WOOD METHOD AND APPARATUS FOR GENERATING CURVES 2 Sheets-Sheet l Filed Nov. 22, 1945 BY m 32.; WW w 22%,

MTORNEYJ Oct. 15, 1946. w, woo 2,409,603

METHOD AND APPARATUS FOR GENERATING CURVES Filed Nov. 22, 1945 2 Sheets-Sheet 2 INVENTOR. E 746w WOr er #1600 BY M 52;

ATTORNEY) Patented Oct. 15,1946

METHOD AND APPARATUS FOR GENERAT- ING CURVES RobertWarner Wood, Princeton, N. J., assignor, by mesne assignments, to Kaiser Fleetwmgs, Inc., a corporation of California Application November 22, 1943, Serial No. 511,291

This invention relates to the generation of curves and particularly to a method and apparatus which are capable of producing second degree curves of the desired contour without the necessity for arduous mathematical calculation.

In industry, curves of varying contour are usein] for many purposes, and particularly in the designing of high speed aircraft second degree curves are employed in effecting the desired streamlining of the exposed surfaces. The method heretofore used to generate such curves involves complex and laborious mathematical calculations. In plants where a multiplicity of different curves is required as the basis for template shapes, modification of design frequently involves additional calculations. These require considerable time of expert mathematicians. Errors sometimes occur in such calculations, involving repetition of the work. The method is therefore a serious item of cost and delay.

t is the object of the invention to provide a simple and effective method of and apparatus for generating second degree curves which are mathematically accurate and available without loss of time for reproduction and use.

Another object of the invention is the provision of a method and apparatus which may be used by a relatively unskilled operator without mathematical training to generate second degree curves having any desired. form.

Other objects and advantages of the invention will be apparent as it is better understood by reference to the following specification and the accompanying drawings, in which Fig. 1 is a diagrammatic illustration in perspective of the principle involved:

Fig. 2 is an elevation illustrating the diffraction hands at the edge of a shadow;

Fig. 3 is a diagram representing the procedure whereby the shape of the desired curve is determined; and

Fig. 4 is a view in perspective illustrating a practical apparatus for the application of the invention.

M invention is based upon the principle that projections of comics are still conics, although the projections may have characteristics difierent from the original. As a simple illustration, if a beam of light from a point source P is projected onto a screen S and an opaque element in the form of a conic, in this instance a circle, is disposed in the beam and rotated partially about an axis aa, a shadow X will be projected upon the screen and will have the form of an 7 Claims. (01. 88-24) ellipse. The minor axis of the ellipse will vary with the angular positionof the opaque element C and'the contour will be changed correspondingly. Instead of a circle, it is possible to use other conic sections such as the ellipse, parabola or hyperbola, and the shadows projected will have the correspondingly varied form, depending upon the shape of the element projected and its angular position. In addition, the element projected may be adjusted angularly about two aXes perpendicular to the axis w-a and its position with respect to the source of light P and. the screen S may be adjusted. It is not essential that the screen S be perpendicular to a line passing through the center of the element C, since it also may be arranged to be tilted about horizontal and vertical axes, although this is not normally necessary for the practice of the invention. In every case, and regardless of the relative adjustment of the element C and the screen S, the projected shadow will be a conic.

It is well known that the edges of shadows are not sharp and well defined but are somewhat fuzzy owing to diffraction. If shadows are produced by a light issuing from a point source,

the phenomenon of difi'raction may easily be observed. Difiraction from the edge of an opaque object takes the form of bands of light and shadow. precisely, but I have endeavored to do so in Fig. 2. in which 5 indicates the shadow, 5 a light band and 1 a dark band beyond which there are a series of light and dark bands merging into the spac 8. These bands are more distinct when the source of light is very small, while the spacing of th bands depends upon the distances from P to C and from C to S. This spacing can be computed accurately. The apparatus can be arranged to make the bands quite narrow, and one of the bands can be selected to'be fitted to the design requirements of the desired second de ree curve.

Although the element C is shown, for purpose of illustration, as an opaque body, the conic section to be projected can, of course, be an opening in an opaque body or it may be delineated as a transparent line or slot in an opaque body, or it may beformed from a thin curved member such as a wire. The only important consideration is that the element C be capable of casting the shadow of a conic section when disposed in a beam of light and rotatable about one or more axes, preferably three, in order to facilitate modification of the curvature of the shadow to fit the desired conditions.

It is difiicult to indicate these bands Just as a straight line is determined uniquely by two points or by one point and a tangent line at that point, a second degree curve is determined uniquely by five points, by four points and a tangent line at one of them, or by three points and tangent lines at two of them. The latter condition is indicated in Fig. 3, in which 9, I and II are predetermined points, and I2 and I 3 tangents at the points 9 and II. The curve M is a conic conforming to these conditions. In designing curved surfaces such, for example, as those used in streamlining airplanes, it is possible to fix the five conditions which determine the desired curve. Heretofore, as already indicated, it has been the practice, when the five conditions have been determined, to proceed by elaborate mathematical calculations, to fix enough remaining points on the curve so that it could be accurately drawn. My invention avoids this difiiculty by the practical application of the principles hereinbefore discussed in the simple apparatus hereinafter described.

Referring to Fig. 4, I5 indicates a housing for a light source such as an are between carbons l6 and H which are supplied with electric current through conductors I8 and I9 from any suitable source. A condenser lens directs a beam of light from the source through a small aperture 2|.

. The housing I5 is connected by a track 22 to an easel 23 carrying a surface 24 which is preferabl white. The easel 23 may be fixed or movable on the track 22. It is preferably movable to permit relative adjustments as may be required.

Between the housing I5 and the easel 23, a block 25 is supported for longitudinal movement along the track 22. It is provided with a groove 26 in which a block 21 is adjustable transversely of the track 22. A standard 28 on the block 21 supports a spindle 29 which is capable of vertical and rotational adjustment and is held in the desired position by a set screw 30. Mounted on the spindle 29 is a frame 3| to which a second frame 32 is pivotally connected at 33. The frame 32 carries a support 34 having a pivot 35 for the element 36 corresponding to the element C of Fig. 1, that is, an element having the outline of a conic section. As will be readily apparent, the element 36 is adjustable about the three axes X, Y and Z of the adjacent diagram by rotating the element on the pivot 35, rotating the frame 32 on the pivots 33 and rotating the spindle 29 on the standard 28. In other words, the element having the outline of the conic section is universally adjustable about the three axes. It also may be moved longitudinally and transversely of the track 22 to vary its relative position with respect to the source of light and the easel 23.

In carrying out the invention, the points 9, I0 and II, and the tangents I2 and I3, which are to determine the desired curve, are marked upon the surface 24. The element 35 is then adjusted about its three axes, and its relative position with respect to the source of light and the easel 23 is modified until the selected diffraction band of the shadow coincides with the points 9, Ill and I I and is tangent to the lines I2 and I3. The resulting outline of the diffraction band is the precis curve desired. If the desired curve cannot be obtained by the described adjustments of the element 36, another element of conic outline may be substituted therefor. Thus, outlines of a circle, ellipse, hyperbola or parabola may be used to secure shadows which are modifications of these conic sections projected upon the surface 24. It is not necessary, of course, to use the entire outline of a conic section. Any selected portion thereof may be projected in the manner described until a curve is found which conforms to 5 the five conditions which are initially marked upon the surface 24.

It remains only to fix the curve of the projected shadow. The simplest procedure when all adustments have been made is to shut off the source of light, substitute a photosensitized surface for the surface 2 and then expose the surface to light from the source for a sufficient interval to secure a photographic image. This operation must be conducted obviously without interference from extraneous light or otherwise in a dark room. Instead of photographing th image, it may be fixed by marking points on the surface 24, which may be subsequently connected to delineate the desired curve. Any other procedure may be utilized to obtain a fixed representation of the curve which may be utilized subsequently in the form of templates or other mechanical means for reproducing the curve. The curve as fixed may be enlarged to any desired scale before it is translated to a template or other device.

The apparatus as illustrated affords the necessary elements in simple form adapted to secure universality of adjustment to reproduce substantially every available second degree curve. Some of the adjustments can, of course, be eliminated where the range of desired second degree curves is limited or where great accuracy is not essential. The elements illustrated need not be in the particular form in which they are shown. For

example, any source of light and means for projecting a beam thereof through a small aperture may be utilized. Many forms of such devices are well known. Likewise, the means for adjusting the element 36 about its three axes and otherwise may be modified, the form illustrated being merel a simple and satisfactory arrangement.

The easel 23 may be supported fixedly or may be made adjustable by any of the ordinary devices available for that purpose.

Various changes may be made, therefore, in the procedure as described and particularly in the apparatus employed without departing from the invention or sacrificing the advantages thereof.

I claim:

0 1. An apparatus for generating curves comprising a plane surface on which a plurality of points not in'a straight line and through which the curve is to pass may be indicated, a support for said surface, a point-light source mounted to project a beam of light toward said surface, a curved outline, a support on which said curved outline is mounted in the beam of light, and

means for adjusting the angle of the plane of said outline relative to the axis of the beam of light.

2. An apparatus for generating curves comprising a plane surface on which a plurality of points not in a straight line and through which th curve is to pass may be indicated, a support for said surface, a point-light source mounted to project a beam of light toward said surface, a curved outline, a support on which said curved outline is mounted in the beam of light, means for adjusting the angle of the plane of said outline relative to the axis of the beam of light, and means for adjusting the support for said outline bodily relatively to the point-light source.

3. An apparatus for generating curves comprising a plane surface on which a plurality of points not in a straight line and through which the curve is to pass may be indicated, a support for said surface, a point-light source mounted to project a beam of light toward said surface, a curved outline, a support on which said curved outline is mounted in the beam of light, and means for adjusting the angle of the plane of said outline about three respectively perpendicular axes relative to the axis of the beam of light.

4. An apparatus for generating curves comprising a plane surface on which a plurality of points not in a straight line and through which the curve is to pass may be indicated, a support for said surface, a point-light source mounted to project a beam of light toward said surface, said surface being mounted substantially normal to the axis of the beam of light, a curved outline, a support on which said curved outline is mounted in the beam of light, and means for adjusting the angle of the plane of the outline relative to the axis of the beam of light.

5. An apparatus for generating curves comprising a plane surface on which a plurality of points not in a straight lin and throuh which the curv is to pass may be indicated, a support for said surface, a point-light source mounted to project a beam of light toward said surface, a curved outline, a support on which said curved line is mounted in the beam of light, and means for adjusting the angle of the plane of said outline, and the 6 angle of the plane of said surface relative to the axis of the beam of light.

6. An apparatus for generating curves comprising a track, a plane surface on which a plurality of points not in a straight line and through which th curve is to pass may be indicated, means for adjustably supporting said surface from said track, a point-light source mounted to project a beam of light toward said surface, a curved outline, a support adjustably mounted on said track on which said curved outline is mounted in the beam of light, and means for adjusting the angle of the plane of said outline relative to the axis of the beam of light.

'7. .An apparatus for generating curves comprising a track, a plane surface on which a plurality of points not in a straight line and through which the curve is to pass may be indicated, a support for said surface, a point-light source mounted to project a beam of light toward said surface, a curved outline, a support on which said curved outline is mounted in the beam of light, said last-named support being mounted on the track and adjustable there along between the point-light source and said plane surface, and means for adjusting the angle of the plane of the outline relative to the axis of the beam of light.

ROBERT WARNER WOOD. 

